Details

Time bar (total: 59.8s)

sample290.0ms

Algorithm
intervals
Results
114.0ms98×body1280valid
96.0ms24×body2560valid
40.0ms56×body640valid
10.0ms22×body320valid
7.0ms44×body80valid
4.0ms12×body160valid

simplify16.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize18.0ms

Local error

Found 2 expressions with local error:

2.0b
(- (tan (+ x eps)) (tan x))
2.9b
(tan (+ x eps))

rewrite448.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×tan-quot add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 tan-sum add-cbrt-cube add-exp-log frac-sub insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 43
Calls
2 calls:
41.0ms
(- (tan (+ x eps)) (tan x))
404.0ms
(tan (+ x eps))

series406.0ms

Counts
2 → 6
Calls
2 calls:
255.0ms
(- (tan (+ x eps)) (tan x))
151.0ms
(tan (+ x eps))

simplify6.7s

Counts
49 → 49
Iterations
IterNodes
done5000
44037
31342
2455
1205
096

prune643.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
2.9b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite346.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
73×add-sqr-sqrt
66×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
9×tan-quot
8×add-cbrt-cube add-exp-log add-log-exp
6×pow1 flip3-- flip--
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l*
3×associate-/r* fma-def associate-*r* associate-*l* associate-/l/
2×flip3-+ frac-add flip-+ difference-of-squares
1×frac-times cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 173
Calls
4 calls:
48.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
21.0ms
(+ (tan x) (tan eps))
43.0ms
(* (tan x) (tan eps))
196.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series2.1s

Counts
4 → 12
Calls
4 calls:
575.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
213.0ms
(+ (tan x) (tan eps))
206.0ms
(* (tan x) (tan eps))
1.1s
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify4.1s

Counts
185 → 185
Iterations
IterNodes
done5003
21635
1581
0242

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.6b

localize167.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sin x) (cos x))
0.2b
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
0.2b
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
2.5b
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

rewrite668.0ms

Algorithm
rewrite-expression-head
Rules
1393×times-frac
890×add-sqr-sqrt
851×*-un-lft-identity
845×add-cube-cbrt
585×prod-diff
106×div-inv
45×fma-neg
30×add-cbrt-cube add-exp-log
28×associate-/r/
26×associate-*r* associate-*l*
15×flip3-- flip--
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod unswap-sqr
6×add-log-exp difference-of-squares
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* associate-/l*
2×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative distribute-lft-out--
1×quot-tan clear-num sub-neg frac-2neg diff-log frac-sub
Counts
4 → 791
Calls
4 calls:
13.0ms
(/ (sin x) (cos x))
57.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
79.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
248.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

series1.4s

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (sin x) (cos x))
292.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
289.0ms
(* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))
713.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

simplify5.0s

Counts
803 → 803
Iterations
IterNodes
done5000
12201
0932

prune9.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.5b

localize291.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ (sin eps) (cos eps)))
0.6b
(cbrt (/ (sin eps) (cos eps)))
0.6b
(cbrt (/ (sin eps) (cos eps)))
2.5b
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

rewrite550.0ms

Algorithm
rewrite-expression-head
Rules
1367×times-frac
851×add-sqr-sqrt
836×*-un-lft-identity
830×add-cube-cbrt
585×prod-diff
104×div-inv
45×fma-neg
39×cbrt-prod
28×associate-/r/
15×flip3-- flip--
6×add-log-exp difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cbrt-div pow1/3
2×distribute-lft-out--
1×sub-neg diff-log frac-sub
Counts
4 → 729
Calls
4 calls:
9.0ms
(cbrt (/ (sin eps) (cos eps)))
10.0ms
(cbrt (/ (sin eps) (cos eps)))
9.0ms
(cbrt (/ (sin eps) (cos eps)))
294.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

series1.7s

Counts
4 → 12
Calls
4 calls:
296.0ms
(cbrt (/ (sin eps) (cos eps)))
360.0ms
(cbrt (/ (sin eps) (cos eps)))
286.0ms
(cbrt (/ (sin eps) (cos eps)))
717.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))

simplify8.2s

Counts
741 → 741
Iterations
IterNodes
done5000
24352
11980
0894

prune6.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.5b

regimes481.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.8b and baseline of 13.0b

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
done34
134
027

end0.0ms

sample8.3s

Algorithm
intervals
Results
4.0s3269×body1280valid
1.6s1897×body640valid
1.5s649×body2560valid
647.0ms761×body320valid
133.0ms1083×body80valid
118.0ms341×body160valid